The Eighth International Workshop on

Matrices and Statistics

Friday 6 August – Saturday 7 August 1999

Tampere, Finland

Satellite Meeting of the 52nd Session of the International

Statistical Institute, Helsinki, 10–18 August 1999

Proceedings to be published in a special issue of the

Linear Algebra and Its Applications.

Address for correspondence: The Workshop Secretary

Dept. of Mathematics, Statistics & Philosophy University of Tampere, P.O. Box 607

FIN-33101 Tampere, FINLAND

Fax: +358-3-2156-157 Email: workshop99@uta.fi

Tel: +358-3-2157-342, (03) 2157-342 (domestic) http://www.uta.fi/~sjp/workshop99.html

Final Programme (as 15 July)

Friday 6 August – Saturday 7 August 1999

Statistics Unit Dept. of Mathematics, Statistics & Philosophy

University of Tampere Tampere, Finland

The Eighth International Workshop on

Matrices and Statistics

4 5

The Eighth International Workshop on

Matrices and Statistics

6—7 August 1999, Tampere, Finland

Proceedings to be published in a special issue of the

Linear Algebra and Its Applications.

Workshop Sponsors

Academy of Finland, City of Tampere, Finnair — The Official Carrier of the Workshop, Foundation for the Promotion of the

Actuarial Profession, International Linear Algebra Society (ILAS Lecturer), Nokia, Pirkanmaa Cultural Foundation,

Ponsse, Research Service Project of the Statistics Unit, Tampere University Foundation, Tixel Software.

Workshop Organization

A local committee within the Statistics Unit of the Dept. of Mathematics, Statistics & Philosophy, Uni-

versity of Tampere

Workshop Address

The Workshop Secretary Dept. of Mathematics, Statistics & Philosophy

University of Tampere, P.O. Box 607 FIN-33101 Tampere, FINLAND

Fax: +358-3-2156-157 Email: workshop99@uta.fi

Tel: +358-3-2157-342, (03) 2157-342 (domestic) http://www.uta.fi/~sjp/workshop99.html

PROGRAMME The Eighth International Workshop on Matrices and Statistics will be held at the University of Tampere on Friday, August 6 and Saturday, August 7, 1999 (starting with a reception on the Thursday evening). This Work-shop is a Satellite Conference of the 52nd Session of the International Statistical Institute to be held in Helsinki from Tuesday, August 10 through Wednesday, August 18, 1999. The purpose of this Eighth Workshop is to stimulate research and, in an informal setting, to foster the in-teraction of researchers in the interface between matrix theory and statistics. This Workshop will provide a fo-rum through which scientists working in the areas of linear algebra/matrix theory and/or statistics may be bet-ter informed of the latest developments and newest tech-niques and may exchange ideas with researchers from several different countries. Selected refereed papers from this Workshop will be published in a Special Issue on Linear Algebra and Statistics of Linear Algebra and Its Applications. The Workshop will include invited and contributed talks, poster session, and a sessions of PhD students.

Opening Session

The Opening Session of the Workshop, chaired by Simo PUNTANEN (University of Tampere) and George P. H. STYAN (McGill University), will be held in Paavo Koli Auditorium of the University of Tampere, on Friday 6 August 1999, starting at 9:00 a.m. Kari-Jouko RÄIHÄ, Vice Rector of the University: Words of welcome on behalf of the University Tapio NUMMI, Head of the Department: Words of welcome on behalf of the Department Furthermore, some words will be said about Profes-sor Bernhard FLURY, who was unexpectedly taken away in a tragic accident in Bolzano, 6 July 1999.

4 5

◆ Keynote Speaker

T. W. ANDERSON, Stanford U, USA: Canonical analysis and reduced rank regression in

autoregressive models

◆ ILAS Lecturer Gene H. GOLUB, Stanford U, USA: Reconstruction of a polygon from its moments (With Peyman Milanfar and James Varah.)

◆ Invited Speakers T. ANDO, Hokusei Gakuen U, Sapporo, Japan: Arithmetic-geometric mean inequalities for matrices Ronald CHRISTENSEN, U of New Mexico, Albuquerque,

USA: Checking the independence assumption in lin-ear models by control charting residuals

Seppo MUSTONEN, U of Helsinki, Finland: Matrix computations in Survo Friedrich PUKELSHEIM, U of Augsburg, Germany: Kiefer ordering of simplex designs for second-degree

mixture models with four or more ingredients (With Norman R. Draper and Berthold Heiligers.) Alastair J. SCOTT, Auckland U, New Zealand: An extension of Richards’ Lemma, with applications

to a class of profile likelihood problems (With Chris Wild.) Shayle R. SEARLE, Cornell U, Ithaca, USA: The infusion of matrices into statistics Bimal K. SINHA, U of Maryland, Baltimore, USA: Nonnegative estimation of multivariate variance

components in unbalanced mixed models George P. H. STYAN, McGill U, Montréal, Canada: Revisiting Hua’s matrix equality and related

inequalities, Schur complements, and Sylvester’s law of inertia (With Christopher C. Paige, Bo-Ying Wang and Fuzhen Zhang.)

◆ Sessions of Contributed Talks

and Posters

For each contributed talk it is reserved 15 minutes, in-cluding discussion. Therefore, if you wish to have com-ments on your presentation, please use less than 15 minutes for your presentation.

■ SESSION C1 Saturday, 13:45–15:00, Room A1 Chair: ANDO, T., Hokusei Gakuen U, Sapporo, Japan AHMED, S. E., U of Regina, Canada: Improved estimation of characteristic roots in princi-

pal analysis DRYGAS, Hilmar, U of Kassel, Germany: Simultaneous SVD: Grillenberger’s approach GROSS, Jürgen, U of Dortmund, Germany: The Moore-Penrose inverse of a partitioned non-

negative definite matrix HAUKE, Jan, Adam Mickiewicz U, Poznan, Poland: On some matrix inequalities and their statistical ap-

plications MERIKOSKI, Jorma K., U of Tampere, Finland: Simple and good bounds for the Perron root TROSCHKE, Sven-Oliver, U of Dortmund, Germany: Quaternions: A matrix oriented approach ■ SESSION C2 Saturday, 13:45–15:00, Room A3 Chair: NUMMI, Tapio, U of Tampere CHAGANTY, N. Rao, Old Dominion U, Norfolk, USA: Statistical analysis of some multivariate models using

quasi-least squares KASALA, Subramanyam, U of North Carolina, Wilming-

ton, USA: An exact joint confidence region and test in multivariate calibration

KLEIN, André, U of Amsterdam, The Netherlands: A generalization of Whittle’s formula

4 5

LIU, Shuangzhe, U of Basel, Switzerland: On maximum likelihood estimation for the VAR-

VARCH model MATHEW, Thomas, U of Maryland, Baltimore County,

Catonsville, USA: Tolerance regions and simultane-ous tolerance regions in multivariate regression

PUNTANEN, Simo, U of Tampere, Finland: In the world of collinearity ... ■ SESSION C3 Saturday, 13:45–15:00, Room A4 Chair: FELLMAN, Johan, Helsinki, Finland CACOULLOS, Theophilos, U of Athens, Creece On testing homoscedasticity via independence under

joint normality FELLMAN, Johan, Swedish S of Econ., Helsinki, Finland: Robust estimators in linear models GNOT, Stanislaw, Pedagogical U, Zielona Gora, Poland: Estimation of variance components by maximum like-

lihood method in certain mixed linear models ISHAK, Maged, U of Newcastle, NSW, Australia: Regression methods to model under registration

problems in population data WERNER, Hans Joachim, U of Bonn, Germany: More on the linear aggregation problem ZMYSLONY, Roman, Technical U, Zielona Gora, Poland: Testing hypotheses for parameters in mixed linear

models ■ SESSION C4 Saturday, 15:15–16:45, Room A1 Chair: JOHN, J. A. (Nye), Hamilton, New Zealand FAREBROTHER, R. W., U of Manchester, UK: Optimality results for the method of averages MARKIEWICZ, Augustyn, Agricult. U of Poznan, Poland: Robust linear estimation in an incorrectly specified restricted linear model JOHN, J. A. (Nye), U of Waikato, Hamilton, New Zea-

land: Recursive formulae for the average efficiency factor in alpha designs

MAROULAS, John, National Technical U, Athens, Greece:

A geometric approach to the canonical correlations in two- and three-way layouts

STEPNIAK, Czeslaw, Agricultural U of Lublin, Poland: Information channels and comparison of linear

experiments ZAIHRAIEV, Oleksandr, N. Copernicus U, Torun, Poland: Distance optimality design criterion and stochastic

majorization ■ SESSION C5 Saturday, 15:15–16:45, Room A3 Chair: LEE, Alan, U of Auckland, New Zealand BENESCH, Thomas, Graz U of Technology, Austria: Internet survey by direct mailing DODGE, Yadolah, U of Neuchâtel, Switzerland: An asymmetric property of the correlation coefficient KOLLO, Tõnu, U of Tartu, Estonia: Density expansions for the sample correlation matrix LEE, Alan, U of Auckland, New Zealand: Generating correlated categorical variates using

Kronecker products TIIT, Ene-Margit, U of Tartu, Estonia: Some extremal properties of correlation matrices VICHI, Maurizio, Soci. Italiana di Statist., Roma, Italy: Least squares approximation of nonpositive semidefi-

nite matrices of correlation coefficients ■ POSTERS AKDENIZ, Fikri, U of Cukurova, Adana, Turkey: The estimation and analysis of residuals for some bi-

ased estimators in linear regression AZEREDO LOPES, Sofia, U of Sheffield, UK: 2D projections of 3D spatial distributions TIAN, Yongge, Concordia U, Montréal, Canada: When do matrix equations have block triangular

solutions? ZONTEK, Stefan, Technical U, Zielona Gora, Poland: On construction of a basis of Jordan algebra of

matrices with applications to a special linear model

4 5

◆ PhD Session Specific sessions on recent PhD- and post-PhD-work on matrices and statistics will be arranged on both days. ■ SESSION PHD1 Friday, 15:00–16:30, Room A1 Chairs: PUKELSHEIM, Friedrich, STYAN, George P. H. ALPARGU, Gülhan, McGill U, Montréal, Canada: Matrices in statistical procedures for valid

hypothesis testing in regression models with autocorrelated errors

DUMAIS, Mylène, McGill U, Montréal, Canada: Some comments and a bibliography on the Craig-

Sakamoto Theorem JENSEN, Shane Tyler, McGill U, Montréal, Canada: Some comments and a bibliography on the von Szö-

kefalvi Nagy–Popoviciu and Nair–Thomson inequali-ties, with extensions and applications to statistics and matrix theory

LU, Chang-Yu, Northeast Normal U, Changchun, Jilin, P. R. China: Some matrix results related to admissi-bility in linear models and generalized matrix ver-sions of Wielandt inequality

KLEIN, Thomas, U of Augsburg, Germany: Optimal de-signs for second degree K-model mixture experiments

NURHONEN, Markku, U of Minnesota, Minneapolis, USA: Matrices related to diagnostic methods in classification problems

■ SESSION PHD2 Saturday, 11:00–12:00, Room A1 Chair: PUKELSHEIM, Friedrich HELLE, Sami, U of Tampere, Finland: Modeling of the fiber length distribution of mechani-

cal pulp using generalized linear models LUOMA, Arto, U of Tampere, Finland: Distance criterion in theory of optimal design OLLIKAINEN, Jyrki, U of Tampere, Finland:

Comparing traditional cluster methods to neural net-works with large medicine data

WEI, Yimin, Fudan U, Shanghai, P. R. China: The modification of the Drazin inverse ■ SESSION PHD2 Saturday, 11:00–12:00, Room A3 Chair: STYAN, George P. H. BORISOV, Mikhail Vladimirovich, Novosibirsk, Russia: The investigation of the stability of two statistical

estimators to complex disturbances in the data GRZADZIEL, Mariusz, Agricultural U of Wroclaw, Poland: On nonnegative quadratic estimation in linear

models TIAN, Yongge, Concordia U, Montréal, Canada: Some universal block-matrix factorizations and their

applications ZHANG, Bao-Xue, Northeast Normal U, Changchun, Jilin,

P. R. China: Some results on estimator of the mean vector and variance in the general linear model and estimating problems for location (scale) models from grouped samples under order restrictions

Workshop Fee The workshop fee is (see the final Registration Form): Before 1 June 1999: FIM 400 Students: FIM 50 After 1 June 1999: FIM 500 Students: FIM 200 Students should provide a confirmation from appropriate university official certifying a full-time student status. The workshop fee includes the Abstract Booklet, en-trance to all sessions, the Thursday-evening reception, and daily coffee breaks. Note that 1 US$ = ca. 5.8 FIM. All participants are required to register on arrival. The registration desk will be at the University Main Building of the University of Tampere on Kalevantie.

4 5

The Bank Account: Account number 800017-37170 with LEONIA BANK, Unioninkatu 22, FIN-00007 Helsinki, SWIFT address: SPBFIHH. The receiver of the Payments should be marked as

Workshop on Matrices/Reference number 43122, Dept. of Mathematics, Statistics & Philosophy, University of Tampere, P.O. Box 607, FIN-33101 Tampere, Finland

Please send also a copy of the receipt of your bank payment by airmail or fax to the Workshop Secretary —thank you in advance!

Organizing Committees

The International Organizing Committee for this Work-shop comprises R. William Farebrother (Victoria Univ. of Manchester, England), Simo Puntanen (Univ. of Tampere; chair), George P. H. Styan (McGill Univ., Montréal, Canada; vice-chair), Hans Joachim Werner (Univ. of Bonn, Germany). The Local Organizing Committee at the University of Tampere comprises Riitta Järvinen, Erkki Liski, Jyrki Ollikainen, Tapio Nummi, and Simo Puntanen (chair), with the assistance of Petri Latva-Rasku, Riina Metsän-oja, and Anne Puustelli. Earlier & Fortcoming Matrix Workshops

This Workshop is the eighth in a series. The previous Workshops were held as follows: (1) Tampere, Finland: August 1990, (2) Auckland, New Zealand: December 1992, (3) Tartu, Estonia: May 1994, (4) Montréal, Québec, Canada: July 1995, (5) Shrewsbury, England: July 1996, (6) Istanbul, Turkey: August 1997. (7) The 7th Workshop was held in Fort Lauderdale,

Florida, USA: 11–14 December 1998, and was in cele-bration of T. W. Anderson’s 80th Birthday. (9) The 9th Workshop will be held in Hyderabad, India: 9-13 December 2000, in celebration of C. R. Rao’s 80th birthday. The program of the Hyderabad event will start with a two-day short course on recent advances in Matrix The-ory, with Special Reference to Application in Statistics, on Saturday, December 9, and Sunday, December 10, 2000. This will be followed by presentation of research papers for the next three days; these papers may then be submitted for publication in a refereed professional re-search journal. Organizing Committees are the following: International: R. W. Farebrother, S. Puntanen (vice-

chair), G. P. H. Styan, H. J. Werner (chair). National: R. Bhatia, P. Bhimasankaram, V. Narayana,

M. Sudhakar Rao, B. G. Sidharth, U. Suryaprakash, R. J. R. Swamy, P. Udayasree, K. Viswanath.

Information about the scientific program can be obtained from: P. Bhimasankaram: pbhim@hotmail.com S. Puntanen: sjp@uta.fi K. Viswanath: kvsm@uohyd.ernet.in H. J. Werner: werner@united.econ.uni-bonn.de Information about registration, deadline for submission of papers and local accommodation can be obtained from: P. Bhimasankaram: pbhim@hotmail.com B. Sidharth: birlasc@hd1.vsnl.net.in R. J. R. Swamy: nhasan@ouastr.ernet.in K. Viswanath: kvsm@uohyd.ernet.in

4 5

Accommodation Blocks of rooms are reserved at the following hotels. All prices are in Finnish marks/night/room. Single Double Sokos Hotel Ilves 670 (530w) 800 (530w) Sokos Hotel Villa 395 (395w) 520 (395w) Lapinkaari 260 (260w) 350* (350*w) w weekends: Fri/Sat, Sat/Sun * 1 + 1 rooms Deadline for hotel reservations: 1 July 1999. Cancella-tions, if needed, should be made by 3 August 1999. All participants should make their own accommoda-tion bookings directly to a corresponding hotel. Early booking is highly recommended. When making the reservation, please mention the Workshop99, University of Tampere. The addresses are: Sokos Hotel Ilves Sokos Hotel Villa Hatanpäänvaltatie 1 Sumeliuksenkatu 14 FIN-33100 Tampere FIN-33100 Tampere fax: +358-(0)3-2626-263 fax: +358-3-2626-268 tel: +358-(0)3-2626-262 tel: +358-3-2626-267 tampere.myyntipalvelut@sok.fi Ilves: www.sokoshotels.fi/english/hotellit/ilves.htm Villa: www.sokoshotels.fi/english/hotellit/villa.htm Kurssihotelli Lapinkaari Lapinkaari 1

Ilves: A high quality hotel in the city centre by the Tam-

merkoski rapids, 1 km from the University, 0.5 km railway station.

Villa: Cosy hotel, offering a friendly and special envi-ronment. The hotel, built in an old grain storehouse, is located by the Tullintori commercial centre, 0.3 km from the University, 0.4 km railway station.

Lapinkaari: This residential hotel offers mainly single rooms with en suite facilities. University, 2.5 km, train station, 2 km.

A bus will operate from the Hotel Ilves and Lapin-

kaari to the University on the Friday and Saturday morn-ings, leaving at 8:30 in front of the hotels’ main en-trances. For other hotels in Tampere, please see the web site www.tampere.fi.

SOCIAL PROGRAMME Welcome Reception

All participants are invited to an informal reception to be held in the Main Building Building of the University of Tampere on Thursday evening at 19:00. The pre-recep-tion speech will be given by Dr X of the Tampere City Health Care and Social Welfare Office, and its prelimi-nary title is “Why do statisticians kiss my toes, or in other words, how close can a statistician get to a Nobel Prize?”

Lunches

The lunch on Friday, the 6th of August, is served at the restaurant of the University's Main Building. The lunch is of buffet type and the price is FIM 35. The buffet lunch on Saturday is in the Restaurant Fuuga of Tampere-talo. The price is FIM 65 and the menu is

Marinated vegetable and mushroom salad Whole grain baguette

... Rosemary-marinated lamb with jalapeno sauce

and sweet pepper potatoes ...

Coffee, tea

The lunch tickets should be bought at the Workshop Desk on a previous day before the lunch. Please note that only limited number of places to lunch to the Restaurant Fuuga are available after 31 July.

4 5

Sauna Party

A Sauna Party in Finnish style (Finns take partying very seriously) will be arranged on Friday evening, the 6th of August, in Viikinsaari Island. The boat leaves from Laukontori Harbour at 18:00. This evening will include a chance to sit three hours in the heat of 80˚C — in which case one loses a lot of sweat, misses the flamed salmon dinner, an international soccer match, and a pleasant stroll around the island. The After-Sauna part of the evening is hosted by Ninni MARTIKAINEN & FINNSTARS. Tarmo PUKKILA, Ex-Rector of the Tampere University, will give an After-Sauna Speech entitled “Is there life outside the universities?” Preliminary programme is as follows: 18:00 The boat leaves from Laukontori

Harbour. 18:15 Arrival at Viikinsaari. 18:20 Welcome Toast. 18:30–18:45 Finland vs Rest of The World — All Star

Teams in Soccer, Viikinsaari Olympic Stadium.

19:00–21:00 Dinner: Flamed salmon. Walk around the island is recommended

(30-40 min). 21:45–22:45 After-Sauna Party in the Restaurant of Vi-

ikinsaari ... along the notes of Ninni Mar-tikainen & Finnstars and the After-Dinner Speech by Tarmo Pukkila.

23:00–23:15 Boat trip back to midtown. 23:30–24:00 Midnight-beer and 'Pumpulitehtaan tytöt',

a dancing performance for hundred seam-stress and sewing machine, in downtown.

You can go to sauna at any time you find convenient from 18:45 to 21:30. There are separate dressing rooms and showers for women and men. The hot part of the sauna (löylyhuone & vihta) is available as follows:

18:45-19:30 Women 19:30-20:00 Men 20:00-20:30 Women 20:30-21:00 Men 21:00-21:30 Women & Men Please take your own swimming suit with you. Towels and beer will be provided. To guarantee your participation in the Sauna Party, the payment FIM 150 should have reached the Workshop Secretary before 1 June 1999. Only a limited number of tickets will be available later on.

Excursions

Excursions, including a city centre walk with Soile Pun-tanen & Evelyn Matheson Styan, for associate partici-pants will be arranged on Friday. Further details avail-able at the workshop desk.

DEADLINES

■ Submission of a preliminary registration form and a tentative title of a contributed paper or a poster:

— in ordinary Session: 10 January 1999 — in the Session of the PhD students: 1 March 1999

■ Request for the financial support for the PhD Student Session: 1 March 1999

■ Abstract: 10 April 1999 ■ Early registration: 1 June 1999

■ Hotel booking: 1 June 1999

HOW TO REACH TAMPERE ?

Tampere, the largest Nordic city without access to the sea — a city of most reserved and introverted people of Finland — is located 170 km north of Helsinki, between Lake Pyhäjärvi and Lake Näsijärvi.

4 5

Trains from Helsinki to Tampere depart hourly. In the IC trains the seat reservation is required. Travel time 2 hours. The train stations of Tampere and Helsinki are right in the city centres. If you arrive at Helsinki Airport, then you may take an Express Bus from the Airport directly to Tampere. Travel time 2.5 hours, departing every 1 - 2 hours. Finn-air buses to Helsinki city centre leave from the airport every 20 minutes between 5:45–1:10. Finnair also offers connections between Helsinki and Tampere. The flight time is 30 minutes. For all timetables, see the links in the Workshop’s web site.

RE-INVENTING REGRESSION THRU GRAPHICS

Thursday, 19 August 1999 As a related activity, a full-day short course on Regres-sion Graphics, by R. Dennis COOK and Sanford WEISBERG

(University of Minnesota, St. Paul, USA) will be arranged in Tampere on Thursday, 19 August 1999. This is a one-day course consisting of six sessions of about one hour each. Textbooks of the course are Cook, R. Dennis and Weisberg, Sanford (1994). An In-

troduction to Regression Graphics. Wiley. Cook, R. Dennis (1998). Regression Graphics: Ideas for

Studying Regressions Through Graphics. Wiley. Furthermore, there is a new Wiley-book entitled Applied Regression Including Computing and Graphics that will correspond exactly to the short course. It is scheduled to be published sometime between August 1st and September 10th Timetable 10:15-13:00 Morning Sessions 13:00-14:15 Lunch 14:15-17:00 Afternoon Sessions 17:15-18:30 Coffee & Tea in the Department

All lectures will be held in Paavo Koli Auditorium of the Pinni Building.

ABSTRACT Regression is the study of the change in a response variable as one or more predictors are varied. It is used in most areas in science, to judge the effectiveness of a treatment, to form prediction equations, and for many other purposes. In this course, we present a new context for regression that requires few scope-limiting assumptions, and a corresponding collec-tion of new methodological tools. Many of these tools use

4 5

simple graphs, along with a well-developed theory, to discover information about the dependence of a response on the predictors. All the methods flow from a few key ideas con-cerning dimension reduction, understanding the role of the distribution of the predictors on the problem, and ways to think about and use graphs in regression analysis. All the methodology discussed will be illustrated with a computer package called R-code that can be used for all the new methods described, and many standard methods for linear regression, nonlinear regression and generalized linear models. A copy of the most recent version of R-code, which runs on the Mac, PC or Unix, will be made available to all workshop participants for use in their own work.

LEARNING OUTCOMES Regression analysis is one of the fundamental tools for the practicing statistician. The traditional role of graphics in re-gression, at least with many predictors, has really been pe-ripheral, dealing mostly with questions of model adequacy. Regression graphics moves graphs to the center of analysis. This requires some new theory, but this theory will be pre-sented at a very general and intuitive level. Our hope is to encourage the participants to use this approach in their own work, and in their own teaching.

REGISTRATION Registration fees: Before 1 June 1999: FIM 300 Students: FIM 30 After 1 June 1999: FIM 400 Students: FIM 200 For further details, see the link in the web site of the Workshop. To guarantee the receipt of the Final Pro-gramme and the Final Registration Form, please take a look at the Workshop’s homepage, or contact the Work-shop Secretary.

––––––––––––––––––––––––––––––––––––– Short Course & Workshop Sponsors

The support of the following sponsors of the Workshop is gratefully acknowledged. Academy of Finland

City of Tampere Finnair — The Official Carrier of the

Workshop Foundation for the Promotion of the Actuarial

Profession International Linear Algebra Society

Nokia Pirkanmaa Cultural Foundation

Ponsse Research Service Project of the Statistics Unit

Tampere University Foundation Tixel Software

–––––––––––––––––––––––––––––––––––––

4 5

List of Participants (15 July 1999) AHMED, S. E., U of Regina, Canada AHONEN, Ilkka, U of Tampere, Finland AKDENIZ, Fikri, U of Cukurova, Adana, Turkey ALPARGU, Gülhan, McGill U, Montréal, Canada ANDERSON, T. W., Stanford U, USA ANDO, T., Hokusei Gakuen U, Sapporo, Japan AZEREDO LOPES, Sofia, U of Sheffield, UK BENESCH, Thomas, Graz U of Technology, Austria BORISOV, Mikhail Vladimirovich, Novosibirsk, Russia BRODSKY, Sergei, Eventus Logistics, Ramat-Gan, Israel CACOULLOS, Theophilos, U of Athens, Creece CHAGANTY, N. Rao, Old Dominion U, Norfolk, USA CHRISTENSEN, Ronald, U of N Mexico, Albuquerque, USA DODGE, Yadolah, U of Neuchâtel, Switzerland DRYGAS, Hilmar, U of Kassel, Germany DUMAIS, Myléne, McGill U, Montréal, Canada FAREBROTHER, R. W., U of Manchester, UK FELLMAN, Johan, Swedish S of Econ., Hki, Finland FIELLER, Nick, U of Sheffield, UK GNOT, Stanislaw, Pedagogical U, Zielona Gora, Poland GOLUB, Gene H., Stanford U, USA GROSS, Jürgen, U of Dortmund, Germany GRZADZIEL, Mariusz, Agricultural U of Wroclaw, Poland HAUKE, Jan, Adam Mickiewicz U, Poznan, Poland HAUKKANEN, Pentti, U of Tampere, Finland HELLE, Sami, U of Tampere, Finland HIETIKKO, Harri, U of Tampere, Finland HUHTALA, Heini, U of Tampere, Finland HUHTANEN, Marko, Helsinki U of Technology, Finland HUUHTANEN, Pentti, U of Tampere, Finland HÄMÄLÄINEN, Petri, U of Tampere, Finland IHALAINEN, Heimo, Tampere U of Technology, Finland ISHAK, Maged, U of Newcastle, NSW, Australia JENSEN, Shane Tyler, McGill U, Montréal, Canada JOHN, J. A. (Nye), U of Waikato, New Zealand JÄRVINEN, Riitta, U of Tampere, Finland KASALA, Subramanyam, U of NC, Wilmington, USA KLEIN, André, U of Amsterdam, The Netherlands

KLEIN, Thomas, U of Augsburg, Germany KOLLO, Tõnu, U of Tartu, Estonia KOREISHA, Sergio, U of Oregon, Eugene, USA KORTE, Heli, U of Tampere, Finland KOSKINEN, Lasse, Centr Pension Sec I, Helsinki, Finland KUOSMANEN, Pauli, Tampere U of Technology, Finland LATVA-RASKU, Petri, U of Tampere, Finland LEE, Alan, U of Auckland, New Zealand LEPPÄLÄ, Raija, U of Tampere, Finland LISKI, Erkki, U of Tampere, Finland LIU, Shuangzhe, U of Basel, Switzerland LU, Chang-Yu, Changchun, P. R. China LUOMA, Arto, U of Tampere, Finland LUUKKAALA, Tiina, U of Tampere, Finland MANNINEN, Pentti, U of Tampere, Finland MARKIEWICZ, Augustyn, Agricult. U of Poznan, Poland MAROULAS, John, National Technical U, Athens, Greece MATHEW, Thomas, U of Maryland, Baltimore, USA MERIKOSKI, Jorma K., U of Tampere, Finland METSÄNOJA, Riina, U of Tampere, Finland MUSTONEN, Seppo, U of Helsinki, Finland MÄKI, Sirkka Liisa, U of Vaasa, Finland MÖTTÖNEN, Jyrki, Tampere U of Technology, Finland NAGI, Ahmed, McGill U, Montréal, Canada NUMMI, Tapio, U of Tampere, Finland NURHONEN, Markku, U of MN, Minneapolis, USA OJA, Hannu, U of Jyväskylä, Finland OLLIKAINEN, Jyrki, U of Tampere, Finland PUKELSHEIM, Friedrich, U of Augsburg, Germany PUKKILA, Tarmo, Min of Soc Aff & Health, Hki, Finland PUNTANEN, Simo, U of Tampere, Finland PUUSTELLI, Anne, U of Tampere, Finland RINGROSE, Trevor John, U of Cranfield, UK SAARELA, Olli, KCL Development Oy, Espoo, Finland SAL MOSLEHIAN, Mohammad, Ferdowsi U, Iran SCOTT, Alastair J., Auckland U, New Zealand SEARLE, Shayle R., Cornell U, Ithaca, USA SILLANPÄÄ, Juha, U of Tampere, Finland SINHA, Bimal K., U of Maryland, Baltimore, USA STEPNIAK, Czeslaw, Agricultural U of Lublin, Poland

4 5

STYAN, George P. H., McGill U, Montréal, Canada TIAMZON III, Terry E., Manila, Philippines TIIT, Ene-Margit, U of Tartu, Estonia TROSCHKE, Sven-Oliver, U of Dortmund, Germany UNTINEN, Helmi, U of Tampere, Finland VEHKALAHTI, Kimmo, U of Helsinki, Finland VICHI, Maurizio, Soci. Italiana di Statist., Rome, Italy VIRTANEN, Ari, U of Tampere, Finland WEI, Yimin, Fudan U, Shanghai, P. R. China WERNER, Hans Joachim, U of Bonn, Germany WILLIAMS, Emlyn, CSIRO, Kingston, Australia ZAIHRAIEV, Oleksandr, N. Copernicus U, Torun, Poland ZHANG, Bao-Xue, Changchun, P. R. China ZMYSLONY, Roman, Technical U, Zielona Gora, Poland ZONTEK, Stefan, Technical U, Zielona Gora, Poland

16